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Thomas Markle, who lives in Mexico, was quoted as telling Los Angeles-based celebrity website TMZ.com that he was scheduled to undergo a heart repair and blockage clearance procedure early on Wednesday morning.
The 73-year-old was due to walk his daughter down the aisle in front of 600 guests including all the senior British royals and a smattering of celebrities on Saturday.
Markle threw the wedding plans into confusion earlier this week when he said he would not attend the nuptials because he did not want to embarrass his daughter or the royal family after reports he had staged pictures with a paparazzi photographer for a fee. He also said he had been hospitalised after suffering a heart attack a week ago.
Harry (33), the Queen grandson and the sixth-in-line to the British throne, and 36-year-old Meghan will marry on Saturday at St George's Chapel in Windsor Castle, the home of English and British monarchs for almost 1000 years.
British newspapers suggested that Meghan's mother Doria Ragland (61), with whom she is spending the night before the ceremony at a nearby luxury hotel, would walk her daughter down the aisle.
On Tuesday, Markle told TMZ that he hated "the idea of missing one of the greatest moments in history and walking my daughter down the aisle."
But he later said doctors had scheduled surgery on Wednesday morning. "They (doctors) will go in and clear blockage, repair damage and put a stent where it is needed," Markle told the website.
Kensington Palace, Harry's office, did not immediately respond to a request for comment on Tuesday. On Monday, it declined to comment on the TMZ report or the father's plans.
"This is a deeply personal moment for Ms Markle in the days before her wedding," Kensington Palace, Harry's office, said in a statement.
"She and Prince Harry ask again for understanding and respect to be extended to Mr Markle in this difficult situation."
The bride-to-be's parents are divorced, and while Harry has been pictured with her Doria Ragland, there had been speculation about how Thomas Markle, a former lighting director for TV soaps and sitcoms, would feature.
He told TMZ that the media attention had taken its toll. He said he had been offered up to $US100,000 ($NZ$145,000) for interviews and been ambushed by paparazzi whose snaps had shown him buying beer and looking dishevelled.
TMZ said he had agreed to the staged pictures, which showed him looking at images of the couple on a computer and being sized up for a suit, because he hoped they would improve his image.
Prince Harry and his elder brother Prince William have both made clear in the past their dislike of the press, fuelled by the death of their mother Princess Diana in a Paris car crash in 1997 as her limousine sped away from chasing paparazzi.
Kensington Palace has limited press access to the ceremony itself and strictly controlled the release of details about the wedding to the media.